1. Field of the Invention
This invention relates to optical data transmission over optical fibers. Specifically, and not by way of limitation, the present invention relates a method and system providing an estimate of the phase of an optical signal during coherent detection.
2. Description of the Related Art
A. Optical Fiber Communications
Information has been transmitted over optical fibers for some time. Details about this field are disclosed in “Optical Communication Systems,” by J. Gowar (Prentice Hall, 2nd ed., 1993) and “Fiber-optic communication systems” by G. P. Agrawal (Wiley, 2nd ed., 1997), which are herein incorporated by reference. The information is usually in the form of binary digital signals, i.e. logical “1”s and “0”s, but fiber optics is also used to transport analog signals, such as cable TV signals. Every optical data transmission system has a transmitter, which emits light modulated with information into the fiber, and a receiver at the far end which detects the light and recovers the information. A long distance digital link may also use one or more digital regenerators at intermediate locations. A digital regenerator receives a noisy version of the optical signal, makes decisions as to what sequence of logical values (“1”s and “0”s) was transmitted, and then transmits a clean noise-free signal containing that information forward towards the destination.
In the 1990's, optical amplifiers were deployed in telephony and cable TV networks, in particular erbium doped fiber amplifiers (EDFAs) were deployed. These devices amplify the optical signals passing through them, and overcome the loss of the fiber without the need to detect and retransmit the signals. A typical long distance fiber optic digital link might contain some digital regenerators between the information source and destination, with several EDFAs in between each pair of digital regenerators. Also in the 1990's, wavelength division multiplexing (WDM) was commercially deployed, which increased the information carrying capacity of the fiber by transmitting several different wavelengths in parallel.
Digital communication systems may include forward error correction (FEC). This field is described in “Error Control Coding: From Theory to Practice” by Peter Sweeney (Wiley, 2002), which is herein incorporated by reference. Block FEC codes are often used with fiber optic transmission systems. At the transmitter, a block of k symbols is coded to a longer block of n symbols, (i.e., overhead is added to the signal). The FEC code is called an (n,k) code. Then, at the receiver, the block of n symbols is decoded back to the original k symbol block. Provided the bit error rate (BER) is not too high, most of the bit errors introduced by the communications channel are corrected. Many fiber optic transmission systems use a standard FEC code based on the Reed-Solomon (255,239) code, as described in ITU-T Standard G.975 “Forward error correction for submarine systems” (International Telecommunication Union, 2000).
B. Direct Detection & Coherent Detection
The transmitter unit for a single WDM channel contains a light source, usually a single longitudinal mode semiconductor laser. Information is imposed on the light by direct modulation of the laser current, or by external modulation, that is by applying a voltage to a modulator component that follows the laser. The receiver employs a photodetector, which converts light into an electric current. There are two ways of detecting the light: direct detection and coherent detection. All the installed transmission systems today use direct detection. Although it is more complex, coherent detection has some advantages, and it was heavily researched into in the 1980s and the start of the 1990s, and has become of interest once again in the past few years.
Most deployed transmission systems impose information on the amplitude (or intensity, or power) of the signal. The light is switched on to transmit a “1” and off to transmit a “0”. In the case of direct detection, the photodetector is presented with the on-off modulated light, and consequently the current flowing through it is a replica of the optical power. After amplification the electrical signal is passed to a decision circuit, which compares it to a reference value. The decision circuit outputs an unambiguous “1” or “0”.
The coherent detection method treats the optical wave more like radio, inherently selecting one wavelength and responding to its amplitude and phase. “Fiber-optic communication systems” by G. P. Agrawal provides an introduction to coherent detection. Coherent detection involves mixing the incoming optical signal with light from a local oscillator (LO) laser source. FIG. 1 illustrates an example of a coherent receiver suitable for detecting a binary phase shift keyed (BPSK) signal. The incoming signal 101 is combined with light 102 from a continuous wave (c.w.) local oscillator in a passive 2:1 combiner 103. The LO light has close to the same state of polarization (SOP) as the incoming signal and either exactly the same wavelength (homodyne detection) or a nearby wavelength (heterodyne detection). When the combined signals are detected at photodetector 104, the photocurrent contains a component at a frequency which is the difference between the signal and local oscillator optical frequencies. This difference frequency component, known as the intermediate frequency (IF), contains all the information (i.e., amplitude and phase) that was on the optical signal. Because the new carrier frequency is much lower, typically a few gigahertz instead of 200 THz, all information on the signal can be recovered using standard radio demodulation methods. Coherent receivers see only signals close in wavelength to the local oscillator, and so by tuning the LO wavelength, a coherent receiver can behave as though having a built-in tunable filter. When homodyne detection is used, the photocurrent is a replica of the information and may be amplified 107 and then passed to the decision circuit 106 which outputs unambiguous “1” or “0” values. With heterodyne detection, the photocurrent must be processed by a demodulator 105 to recover the information from the IF. FIG. 1 illustrates a configuration for single-ended detection. There are other configurations for coherent detection. For example, a balanced detection configuration is obtained by replacing the 2:1 combiner by a 2:2 combiner, each of whose outputs are detected and the difference taken by a subtracting component.
Following is a mathematical description of the coherent detection process. (The complex notation for sinusoids is summarised in the Appendix.) The electric field of the signal may be written asRe└Es(t)eiωst+iφs(t)┘where Es(t) is the slowly varying envelope containing the information encoded on amplitude and phase of the optical signal, ωs is the angular frequency of the optical carrier, and φs(t) is the slowly varying phase noise associated with the finite linewidth of the laser. Writing the phase noise separate from the modulation envelope Es(t) has the advantage that in the case of digital information transmission Es(t) takes on only a small number of possible values, depending on the digital signal format. Similarly, the electric field of the local oscillator is written asRe└ELOeiωLOt+iφLO(t)┘where ELO is a constant given that the local oscillator is c.w., ωLO is the angular frequency of the LO, and φLO(t) is the phase noise on the LO. The electric fields of the signal and LO are written as scalar quantities because it is assumed that they have the same state of polarization. The electric field of the light arriving at the photodetector 104 in FIG. 1 is the sum of the two electric fieldsE1=Re└Es(t)ei(ωst+φs(t))+ELOei(ωLOt+φLO(t))┘and the optical power isP1=E1*E1 P1=|Es(t)|2+|ELO|2+2Re[Es(t)ELO*ei(ωs−ωLO)t+i(φs(t)−φLO(t))]  (1)In the case of single ended detection only one output of the combiner is used. |ELO|2 is constant with time. |Es(t)|2 is small given that the local oscillator power is much larger than the signal power, and for phase shift keying (PSK) and frequency shift keying (FSK) modulation formats |Es(t)|2 is constant with time. The dominant term in equation 1 is the beat term Re└Es(t)LO*ei(ωs−ωLO)t+i(φs(t)−φLO(t))┘. In appropriate conditions the beat term can be readily obtained from the photocurrent in the single-ended detection case. Alternatively, when |Es(t)|2 is not small and varies with time, the beat term is produced directly by the balanced detection configuration. The equations that follow refer to the beat term. It is assumed that this term is obtained by single ended detection given that the other terms do not contribute or by balanced detection.
There are two modes of coherent detection: homodyne and heterodyne. In the case of homodyne detection the frequency difference between signal and local oscillator is zero, and the local oscillator laser has to be phase locked to the incoming signal in order to achieve this. For homodyne detection the term ei(ωs−ωLO)t+i(φs(t)−φLO(t)) is 1, and the beat term becomesRe└Es(t)ELO*┘For the binary phase shift keying (BPSK) modulation format for example, Es(t) takes on the value 1 or −1 depending on whether a logical “1” or “0” was transmitted, and the decision circuit can simply act on the beat term directly.
With heterodyne detection there is a finite difference in optical frequency between the signal and local oscillator. All the amplitude and phase information on the signal appears on a carrier at angular frequency (ωs−ωLO), the intermediate frequency, and it can be detected with a demodulator using standard radio detection methods. Typically homodyne detection gives better performance than heterodyne detection, but is harder to implement because of the need for optical phase locking. Heterodyne detection can be further divided into two categories: synchronous and asynchronous. With synchronous heterodyne detection the receiver makes an estimate of the optical phase difference between the incoming optical signal and the light from the local oscillator, and applies the phase estimate during the digital decision making process. An asynchronous heterodyne detection receiver does not make an estimate of the phase. The data is obtained via another method, depending on which modulation format was used, such as by taking the difference between one digital symbol and the next (differential detection). Synchronous detection gives better receiver sensitivity than asynchronous detection. Homodyne detection can be considered to be a synchronous coherent detection method, because the process of optical phase locking the local oscillator requires a phase estimate to be made.
C. Sampled Coherent Detection
A new method of coherent detection called sampled coherent detection has been proposed and demonstrated recently, as described in U.S. Patent Application No. 2004/0114939 and in “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments” by M. G. Taylor (IEEE Phot. Tech. Lett., vol. 16, no. 2, p. 674-676, 2004), which are herein incorporated by reference. Digital signal processing (DSP) is employed in this method to obtain the information carried by a signal from the beat products seen at the outputs of a phase diverse hybrid. The field of digital signal processing is summarized below.
In sampled coherent detection, the signal and local oscillator are combined in a passive component called a phase and polarization diverse hybrid. FIG. 2 shows a sampled coherent detection apparatus. The four outputs of the phase and polarization diverse hybrid are detected by separate photodetectors 212 and then, after optional amplification by amplifiers 213, they are sampled by A/D converters 214. The sample values of the A/D converters are processed by the digital signal processor 215 to calculate the complex envelope of the signal electric field over time. The phase and polarization diverse hybrid has four outputs 208-211 in the example of FIG. 2, where single ended detection is used. The top two outputs 208 and 209 have the LO in one state of polarization, e.g., the horizontal polarization, and the lower two outputs 210 and 211 have the LO in the orthogonal, vertical, polarization. For each of the two LO polarization states, the signal is combined with the LO in a 90° hybrid 205, also known as a phase diverse hybrid. The phase of the LO relative to the signal in one output of the 90° hybrid is different by π/2 radians (i.e. 90°) compared to the phase of the LO relative to the signal in the other output. This phase shift can be implemented by extra path length in one arm 207 of the 90° hybrid carrying the LO compared to the other arm 206, as can be seen in FIG. 2. The orthogonal SOP relationship between the two 90° hybrids is achieved by using a polarization beamsplitter 204 to divide light from the local oscillator 202 between the two hybrids and a standard 1:2 splitter 203 to divide the incoming signal light 201.
The following mathematical treatment explains how the electric field of the signal is obtained from the outputs of the phase and polarization diverse hybrid. The incoming signal electric field can be written asRE└Es(t)eiωst+iφs(t)┘where Es(t) is a Jones vector, a two-element vector comprising the polarization components of the electric field in the horizontal and vertical directions. The use of Jones vectors is summarised in the Appendix.
            E      s        ⁡          (      t      )        =      (                                                      E              sx                        ⁡                          (              t              )                                                                                      E              sy                        ⁡                          (              t              )                                            )  Each of the four outputs of the phase and polarization diverse hybrid in FIG. 2 contains signal Re┘Es(t)eiωxt+iφs(t)┘. The local oscillator in the four outputs is different, and can be written as followstop output . . . Re└ELOeiωLOt+iφLO(t){tilde over (x)}┘2nd output . . . Re└i ELOeiωLOt+iφLO(t){tilde over (x)}┘3rd output . . . Re└ELOeiωLOt+iφLO(t){tilde over (y)}┘4th output . . . Re└i ELOeiωLOt+iφLO(t){tilde over (y)}┘In the top two arms the LO is horizontally polarized, in the direction of Jones unit vector {tilde over (x)}, and in the lower two arms vertical in the direction of {tilde over (y)}. The π/2 phase shift is accounted for by the multiplicative imaginary number i. The beat term parts of the optical powers in the four outputs 208 through 211 are thereforebeat term 1=Re└Esx(t)ELO*ei(ωs−ωLO)t+i(φs(t)−φLO(t))┘beat term 2=Im└Esx(t)ELO*ei(ωs−ωLO)t+i(φs(t)−φLO(t))┘beat term 3=Re└Esy(t)ELO*ei(ωs−ωLO)t+i(φs(t)−φLO(t))┘beat term 4=Im└Esy(t)ELO*ei(ωs−ωLO)t+i(φs(t)−φLO(t))┘It follows that the envelope of the signal electric field is related to the observed beat terms by
                                          E            s                    ⁡                      (            t            )                          =                                            ⅇ                                                                    -                                          ⅈ                      ⁡                                              (                                                                              ω                            s                                                    -                                                      ω                            LO                                                                          )                                                                              ⁢                  t                                -                                  ⅈ                  ⁡                                      (                                                                                            ϕ                          s                                                ⁡                                                  (                          t                          )                                                                    -                                                                        ϕ                          LO                                                ⁡                                                  (                          t                          )                                                                                      )                                                                                      E              LO              *                                ⁢                      (                                                                                                      (                                              beat                        ⁢                                                                                                  ⁢                        term                        ⁢                                                                                                  ⁢                        1                                            )                                        +                                          ⅈ                      ⁡                                              (                                                  beat                          ⁢                                                                                                          ⁢                          tterm                          ⁢                                                                                                          ⁢                          2                                                )                                                                                                                                                                                    (                                              beat                        ⁢                                                                                                                                  ⁢                                                                                                                                ⁢                        term                        ⁢                                                                                                  ⁢                        3                                            )                                        +                                          ⅈ                      ⁡                                              (                                                  beat                          ⁢                                                                                                          ⁢                          term                          ⁢                                                                                                          ⁢                          4                                                )                                                                                                                  )                                              (        2        )            In order to implement equation 2, the frequency difference as ωs−ωLO and phase difference φs(t)−φLO(t) must be known. The digital signal processor must make estimates of these quantities and apply these to make an estimate of the signal electric field envelope.
                                                        E              ^                        s                    ⁡                      (            t            )                          =                                            ⅇ                                                                    -                    ⅈ                                    ⁢                                      ω                    ^                                    ⁢                  t                                -                                  ⅈ                  ⁢                                                            ϕ                      ^                                        ⁡                                          (                      t                      )                                                                                                          E              LO              *                                ⁢                      (                                                                                                      (                                              beat                        ⁢                                                                                                  ⁢                        term                        ⁢                                                                                                  ⁢                        1                                            )                                        +                                          ⅈ                      ⁡                                              (                                                  beat                          ⁢                                                                                                          ⁢                          term                          ⁢                                                                                                          ⁢                          2                                                )                                                                                                                                                                                    (                                              beat                        ⁢                                                                                                  ⁢                        term                        ⁢                                                                                                  ⁢                        3                                            )                                        +                                          ⅈ                      ⁡                                              (                                                  beat                          ⁢                                                                                                                                            ⁢                                                                                                                                          ⁢                          term                          ⁢                                                                                                                                            ⁢                                                                                                                                          ⁢                          4                                                )                                                                                                                  )                                              (        3        )            Ês(t) is an estimate of the true signal electric field envelope Es(t), and the decision of the data carried by the signal is derived from Ês(t). {circumflex over (ω)} is an estimate of the angular frequency difference ωs−ωLO. {circumflex over (φ)}(t) is an estimate of the optical phase difference between signal and local oscillator φs(t)−φLO(t). Clearly if the estimates {circumflex over (ω)} and {circumflex over (φ)}(t) are exactly correct, then equation 3 becomes equation 2, and the estimate of the signal electric field envelope Ês(t) is equal to the true envelope Es(t). Conversely, any inaccuracy in the estimates {circumflex over (ω)} and {circumflex over (φ)}(t) leads to errors in the received digital data. The object of the present invention is to make an accurate phase estimate within the digital signal processor.
The digital information is imposed on the signal electric field envelope as a sequence of symbols regularly spaced in time. To recover the information the digital signal processor must also have an estimate of the times of the symbol centers (i.e., a symbol clock).
Transmission over a length of optical fiber transforms the state of polarization of an optical signal, so that the digital values taken on by Es(t) as seen at the receive end of a fiber optic transmission system are typically not the same as those imposed at the transmit end. The polarization transformation can be reversed within the DSP by multiplying by the appropriate rotation Jones matrix R, so that the first element of the Jones vector contains the complex envelope of an information-bearing signal.
                                                        E              ^                        s                    ⁡                      (            t            )                          =                                            ⅇ                                                                    -                    ⅈ                                    ⁢                                      ω                    ^                                    ⁢                  t                                -                                  ⅈ                  ⁢                                                            ϕ                      ^                                        ⁡                                          (                      t                      )                                                                                                          E              LO              *                                ⁢                                    x              ~                        ·                          R              ⁡                              (                                                                                                                              (                                                      beat                            ⁢                                                                                                                  ⁢                            term                            ⁢                                                                                                                  ⁢                            1                                                    )                                                +                                                  ⅈ                          ⁡                                                      (                                                          beat                              ⁢                                                                                                                          ⁢                              term                              ⁢                                                                                                                          ⁢                              2                                                        )                                                                                                                                                                                                                            (                                                      beat                            ⁢                                                                                                                  ⁢                            term                            ⁢                                                                                                                  ⁢                            3                                                    )                                                +                                                  ⅈ                          ⁡                                                      (                                                          beat                              ⁢                                                                                                                                                                ⁢                                                                                                                                                              ⁢                              term                              ⁢                                                                                                                          ⁢                              4                                                        )                                                                                                                                              )                                                                        (        4        )            (Ês(t) is written without boldface because it represents a complex electric field without regard to polarization, and not a Jones vector.) The correct rotation matrix R can be estimated by exploring the available space and then locking on to the matrix which gives the best quality signal. The polarization transformation of the optical fiber typically changes slowly, so the rotation matrix must be allowed to update. Alternatively the SOP of the local oscillator can be matched to that of the signal by a hardware polarization controller, so that equation 3 need be implemented only for one element of the Jones vector Es(i), based on two phase diverse hybrid outputs instead of four.
                                                        E              ^                        s                    ⁡                      (            t            )                          =                                            ⅇ                                                                    -                    ⅈ                                    ⁢                                      ω                    ^                                    ⁢                  t                                -                                  ⅈ                  ⁢                                                            ϕ                      ^                                        ⁡                                          (                      t                      )                                                                                                          E              LO              *                                ⁢                      (                                          (                                  beat                  ⁢                                                                          ⁢                  term                  ⁢                                                                          ⁢                  1                                )                            +                              ⅈ                ⁡                                  (                                      beat                    ⁢                                                                                  ⁢                    term                    ⁢                                                                                  ⁢                    2                                    )                                                      )                                              (        5        )            
The Jones vector Es(t) constitutes a complete description of the optical signal, or more precisely of the signal's optical spectrum in the region of the local oscillator. This means that any parameter of the optical signal can be deduced from Es(t). Employing sampled coherent detection is more complex than direct detection, but has many benefits. Phase encoded modulation formats can be employed, such as BPSK and quadrature phase shift keying (QPSK), which offer better sensitivity than on-off modulation formats. Also polarization multiplexed formats can be employed, which offer twice the information capacity for a given bandwidth of electro-optic components and a given optical spectral bandwidth. The polarization demultiplexing operation is performed within the digital signal processor, so no additional optical components are needed for it. In a long fiber optic transmission system carrying high bit rate signals, the optical fiber propagation effects, such as chromatic dispersion and polarization mode dispersion, distort the signals. With sampled coherent detection, the propagation effects can be reversed within the DSP by applying an appropriate mathematical operation. Finally, a key benefit of sampled coherent detection is that it is equivalent to passing the signal through a narrow optical filter centred on the local oscillator wavelength, so no narrow optical filter components are needed for WDM. The LO can be tuned in wavelength, which is equivalent to tuning the optical filter.
D. Digital Signal Processing
The present invention utilizes digital signal processing (DSP). DSP is described in “Understanding Digital Signal Processing” by R. G. Lyons (Prentice Hall, 1996) and “Digital Signal Processing: Principles, Algorithms and Applications” by J. G. Proakis & D. Manolakis (Prentice Hall, 3rd ed., 1995), herein incorporated by reference. A signal processor is a unit which takes in a signal, typically a voltage vs. time, and performs a predictable transformation on it, which can be described by a mathematical function. FIG. 3a shows a generic analog signal processor (ASP). The box 302 transforms the input signal voltage 301 into the output signal voltage 303, and may contain a circuit of capacitors, resistors, inductors, transistors, etc. FIG. 3b illustrates a digital signal processor. First, the input signal 301 is digitized by the analog to digital (A/D) converter 304, that is converted into a sequence of numbers, each number representing a discrete time sample. The core processor 305 uses the input numerical values to compute the required output numerical values, according to a mathematical formula that produces the required signal processing behavior. The output values are then converted into a continuous voltage vs. time by the digital to analog (DIA) converter 306. Alternatively, for applications in a digital signal receiver, the analog output of the DSP may go into a decision circuit to produce a digital output. In such a situation, the digital processing core may perform the decision operation and output the result, in which case the D/A converter 306 is not needed.
The digital filter is an operation that may be executed in a digital signal processor. A sequence of filtered output values Y(n), n=0, 1, 2, 3 . . . , is calculated from input values X(n) by
                              Y          ⁡                      (            n            )                          =                                            ∑                              k                =                0                            B                        ⁢                                          b                ⁡                                  (                  k                  )                                            ⁢                              X                ⁡                                  (                                      n                    -                    k                                    )                                                              +                                    ∑                              k                =                1                            A                        ⁢                                          a                ⁡                                  (                  k                  )                                            ⁢                              Y                ⁡                                  (                                      n                    -                    k                                    )                                                                                        (        6        )            The b(k) are known as feedforward tap weights, and the a(k) are feedback tap weights. The digital filter of equation 6 may be written in terms of a z-transfer function
      Y    ⁡          (      z      )        =                              ∑                      k            =            0                    B                ⁢                              b            ⁡                          (              k              )                                ⁢                      z                          -              k                                                  1        -                              ∑                          k              =              1                        A                    ⁢                                    a              ⁡                              (                k                )                                      ⁢                          z                              -                k                                                          ⁢          X      ⁡              (        z        )            X(z) and Y(z) are the z-transforms of X(n) and Y(n) respectively.
The applications of digital signal processing in optical coherent detection of communications signals may be such that the clock speed of the logic in the digital signal processor is slower than the symbol rate at which information is transmitted. For example, the DSP clock speed may be 10 GHz while the information signaling rate is 10 Gbaud. This means that the DSP must operate in parallel (FIG. 3C). The incoming symbols are first demultiplexed into parallel branches 307a, 307b, 307c, 307d, and then each branch is processed at the low logic clock speed. A constraint of such a parallel architecture is that symbol n−1 may be processed at the same time as symbol n, so the result of an operation on symbol n−1 is not available at the commencement of the operation on symbol n. Many signal processing algorithms feed back the result of operation n−1 to calculate operation n. Such an algorithm cannot be implemented in a parallel digital processor. The parallel operation of the DSP is equivalent to imposing a delay on any feedback paths. It is an object of the present invention to estimate the optical phase in the digital signal processor without using feedback from immediately preceding results, but instead employing algorithms that do not use any feedback or that use feedback from distant past results.
E. Existing Phase Estimation Methods
Digital communications over radio and electrical cables has led to the development of methods for estimation of the phase of the carrier of a narrowband signal. Many of these methods are described in “Digital Communications” by J. G. Proakis (McGraw-Hill, 4th ed., 2000), “Digital communication receivers: synchronization, channel estimation & signal processing” by H. Meyr, M. Moeneclaey & S. A. Fechtel (Wiley, 1998) and “Synchronization techniques for digital receivers” by U. Mengali & A. N. D'Andrea (Plenum Press, 1997), which are herein incorporated by reference. The delay to the times of the symbol centers, the frequency difference between the signal and local oscillator and the phase of the signal compared to the local oscillator are collectively known as reference parameters or as synchronization parameters. With coherent optical detection there is an additional reference parameter: the state of polarization of the signal compared to the LO. The best possible estimate of a reference parameter that can be made based on the noisy observations is known as the optimal estimate. If a reference parameter changes unpredictably, but these changes are slow, then it is possible to use an estimate which deviates from the optimal estimate without causing a significant increase in the number of errors in the detected digital information. Also an algorithm with feedback to distant past results may be used. This means that a simple algorithm convenient for implementation in the DSP may be chosen to estimate a slowly varying reference parameter. However, it is important to make an estimate close to the optimal estimate for a reference parameter that changes rapidly on the time scale of the symbol period, otherwise there will be a substantial increase in the bit error rate. In a typical implementation of coherent detection of optical signals, the symbol clock, the frequency difference between signal and local oscillator, and the SOP of the signal all vary slowly. Techniques are available to estimate these parameters. However, the optical phase of the signal compared to the local oscillator may vary rapidly and randomly, unless expensive narrow linewidth lasers are used. A near optimal estimate of the phase is therefore needed. It is clear that any phase estimation method from the field of radio can be applied to optical coherent detection. However there is no application in radio with the same level of phase noise as with optical coherent detection. In a possible configuration using decision feedback (DFB) lasers, the combined laser linewidth Δν may be 10 MHz and the signaling rate 10 Gbaud, so that the product of symbol time and linewidth is τxΔν=10−3. There are no examples in the prior art having such a high τsΔν, and the methods used in radio cannot be applied to optical coherent detection.
Experiments were performed with synchronous optical coherent detection in the early 1990's which inherently made an estimate of the phase. Examples are “4-Gb/s PSK Homodyne Transmission System Using Phase-Locked Semiconductor Lasers” by J. M. Kahn et al. (IEEE Phot. Tech. Lett., vol. 2, no. 4, p. 285-287, 1990) and “An 8 Gb/s QPSK Optical Homodyne Detection Experiment Using External-Cavity Laser Diodes” by S. Norimatsu et al. (IEEE Phot. Tech. Lett., vol. 4, no. 7, p. 765-767, 1992). These experiments used continuous time analog signal processing, but it is clear that an equivalent discrete time algorithm could be derived from the analog signal processing function. The experiments used decision directed detection and phase locked loops, both of which use feedback. In the experiments the feedback paths were kept purposely short. It was known that long feedback delay times imposed a requirement for narrow linewidth lasers, as is discussed in “Damping factor influence on linewidth requirements for optical PSK coherent detection systems” by S. Norimatsu & K. Iwashita (IEEE J. Lightwave Technol., vol. 11, no. 7, p. 1226-1233, 1993). In a DSP implementation the effective length of the feedback path is constrained by the clock frequency of the DSP logic. Also the experiments used external cavity lasers having low linewidth instead of less expensive integrated semiconductor lasers, such as DFB lasers. So the techniques used in these optical coherent detection experiments do not provide a solution for implementing optical coherent detection using digital signal processing with inexpensive wide linewidth lasers.
“PLL-Free Synchronous QPSK Polarization Multiplex/Diversity Receiver Concept With Digital I&Q Baseband Processing” by R. Noé (IEEE Phot. Tech. Lett., vol. 17, no. 4, p. 887-889, 2005) discloses a phase estimation method for optical coherent detection using digital signal processing, which is suitable for a parallel DSP because it does not employ feedback. The method has been implemented experimentally in “Unrepeatered optical transmission of 20 Gbit/s quadrature phase-shift keying signals over 210 km using homodyne phase-diversity receiver and digital signal processing” by D.-S. Ly-Gagnon et al. (IEE Electron. Lett., vol. 41, no. 4, p. 59-60, 2005). This phase estimation method involves applying a fourth power nonlinearity and then taking a simple average of complex field values of a group of contiguous symbols, which is equivalent to planar filtering with a rectangular time response filter. The rectangular time response filter is chosen because it does not employ feedback. However, this filter shape is not close to the optimal filter shape, which increases the bit error rate. Differential logical detection is used after decisions are made to avoid the impact of cycle slips, but it has the disadvantage that it increases the bit error rate. Another disadvantage is that every time the filter complex output crosses the negative real boundary (every time a cycle count occurs) an extra symbol error is inserted, which leads to a background bit error rate even when the transmission system additive noise is low. It would be better to include a cycle count function to avoid the effect of cycle slips, but cycle count functions use feedback.
Although not proposed for applications like optical coherent detection where the oscillators have high linewidth, there are phase estimation solutions in the field of radio that work with a randomly varying phase. A method is disclosed in “Digital communication receivers: synchronization, channel estimation & signal processing” by H. Meyr et al. where the complex field is operated on by a nonlinear function and then passed to a planar filter having transfer function
      H    ⁡          (      z      )        =            1      -              α        pp                    1      -                        α          pp                ⁢                  z                      -            1                              This is similar to the zero lag Wiener filter phase estimation method of the present invention which is described below, and has the transfer function of equation 13. However the disclosure does not identify how to choose αpp to obtain a close approximation to the optimal zero-lag phase estimate. Also the transfer function involves feedback to the immediately preceding result, and the disclosure does not explain how to implement the filter in a parallel digital signal processor. The same disclosure describes how to unwrap the phase of the planar filter output by using a cycle count function. The basic equation of the phase unwrapping method is the same as equation 22 that is used in the present invention, described below. However the cycle count function in the disclosure (and that of equation 22) employs feedback from the immediately preceding result, and the disclosure does not explain how to implement the cycle count function in a parallel digital signal processor.
Thus there is a need for a phase estimation method that can be implemented in a parallel digital signal processor architecture, and which does not use feedback from recent results. There is also a further need for such a phase estimation method to provide an estimate which is close to the optimal phase estimate. It is an object of the present invention to provide such a methodology and system.